Monday, July 17, 2006
SF: Definitely a new factoring method
Ok, so now wasn't that fun! Several years of effort with lots of very crappy and even stupid ideas under the bridge but now there is a new factoring method.
The method is given a target composite T, you can search for x and y such that
x^2 - y^2 = 0 mod T
by picking x_res and S, to solve for a variable k, where
k = S*(2*x)^{-1} mod T
and
x+k = sqrt(S+k^2 + y^2)
so finding x and y is just a matter of factoring S+k^2, so it is, indeed, a surrogate factoring method.
It has been shown to work by a Tim Peters, who has also been certain that it can't be made practical, but that is irrelevant to the question of it definitely being a new factoring method.
So even from the "pure math" aspect, the event here is significant.
The achievement was the result of lateral thinking, wondering if it might be possible to factor one number by instead factoring another, which I call surrogate factoring.
Surrogate factoring has been achieved.
The continuing debate is over its effectiveness.
I am no longer talking out research on Usenet.
I have contacted the U.S. military and we'll see how it goes. They may just think I'm a crackpot.
Others may feel free to play with these ideas as they see fit, as of course, I couldn't stop you anyway.
Now it's your math.
[A reply to someone who said that, even if it works, it will be useless if it is not efficient.]
That's a practical argument.
I'm making a "pure math" argument.
Besides, there are very few known factoring methods, despite what some of you seem to think from your replies to me, as if there are these things all over the place.
Look it up.
Now there is one more to add to those you can read about in references.
The achievement is fairly huge, whether it's practical or not.
New ideas are just not that easy to come by in modern mathematics.
I know a lot of you hate me, but reality is, what it is.
So a person you hate makes discoveries. Deal with it.
Or, you can choose to betray your discipline clearly in an area where there is no doubt what you're doing where I can maybe pull worldwide attention because of the status of the problem.
I don't care any more.
If you people wish to be one way with research from people you like and then another with someone you hate, then fine, I'll do my best to make sure you face consequences, as either you love mathematics, or you're liars anyway, who played a line that sounded good to you and the world.
The method is given a target composite T, you can search for x and y such that
x^2 - y^2 = 0 mod T
by picking x_res and S, to solve for a variable k, where
k = S*(2*x)^{-1} mod T
and
x+k = sqrt(S+k^2 + y^2)
so finding x and y is just a matter of factoring S+k^2, so it is, indeed, a surrogate factoring method.
It has been shown to work by a Tim Peters, who has also been certain that it can't be made practical, but that is irrelevant to the question of it definitely being a new factoring method.
So even from the "pure math" aspect, the event here is significant.
The achievement was the result of lateral thinking, wondering if it might be possible to factor one number by instead factoring another, which I call surrogate factoring.
Surrogate factoring has been achieved.
The continuing debate is over its effectiveness.
I am no longer talking out research on Usenet.
I have contacted the U.S. military and we'll see how it goes. They may just think I'm a crackpot.
Others may feel free to play with these ideas as they see fit, as of course, I couldn't stop you anyway.
Now it's your math.
[A reply to someone who said that, even if it works, it will be useless if it is not efficient.]
That's a practical argument.
I'm making a "pure math" argument.
Besides, there are very few known factoring methods, despite what some of you seem to think from your replies to me, as if there are these things all over the place.
Look it up.
Now there is one more to add to those you can read about in references.
The achievement is fairly huge, whether it's practical or not.
New ideas are just not that easy to come by in modern mathematics.
I know a lot of you hate me, but reality is, what it is.
So a person you hate makes discoveries. Deal with it.
Or, you can choose to betray your discipline clearly in an area where there is no doubt what you're doing where I can maybe pull worldwide attention because of the status of the problem.
I don't care any more.
If you people wish to be one way with research from people you like and then another with someone you hate, then fine, I'll do my best to make sure you face consequences, as either you love mathematics, or you're liars anyway, who played a line that sounded good to you and the world.
# posted by James Harris @ 21:22 
